{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 基尼系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data[:,2:]\n",
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None, criterion='gini',\n                       max_depth=2, max_features=None, max_leaf_nodes=None,\n                       min_impurity_decrease=0.0, min_impurity_split=None,\n                       min_samples_leaf=1, min_samples_split=2,\n                       min_weight_fraction_leaf=0.0, presort='deprecated',\n                       random_state=42, splitter='best')"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "dt_clf = DecisionTreeClassifier(max_depth=2, criterion=\"gini\", random_state=42)\n",
    "dt_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_decision_boundary(model, axis):\n",
    "    \n",
    "    x0, x1 = np.meshgrid(\n",
    "        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*200)).reshape(-1, 1),\n",
    "        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*200)).reshape(-1, 1),\n",
    "    )\n",
    "    X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "    y_predict = model.predict(X_new)\n",
    "    zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "    from matplotlib.colors import ListedColormap\n",
    "    custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])\n",
    "    \n",
    "    plt.contourf(x0, x1, zz, cmap=custom_cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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364.903125 202.665863 \r\nL 364.903125 202.302858 \r\nL 364.903125 201.939853 \r\nL 364.903125 201.576848 \r\nL 364.903125 201.213843 \r\nL 364.903125 200.850838 \r\nL 364.903125 200.487833 \r\nL 364.903125 200.124828 \r\nL 364.903125 199.761823 \r\nL 364.903125 199.398818 \r\nL 364.903125 199.035813 \r\nL 364.903125 198.672808 \r\nL 364.903125 198.309803 \r\nL 364.903125 197.946798 \r\nL 364.903125 197.583793 \r\nL 364.903125 197.220788 \r\nL 364.903125 196.857783 \r\nL 364.903125 196.494778 \r\nL 364.903125 196.131773 \r\nL 364.903125 195.768768 \r\nL 364.903125 195.405763 \r\nL 364.903125 195.042758 \r\nL 364.903125 194.679753 \r\nL 364.903125 194.316748 \r\nL 364.903125 193.953743 \r\nL 364.903125 193.590738 \r\nL 364.903125 193.227733 \r\nL 364.903125 192.864728 \r\nL 364.903125 192.501723 \r\nL 364.903125 192.138718 \r\nL 364.903125 191.775713 \r\nL 364.903125 191.412708 \r\nL 364.903125 191.049703 \r\nL 364.903125 190.686698 \r\nL 364.903125 190.323693 \r\nL 364.903125 189.960688 \r\nL 364.903125 189.597683 \r\nL 364.903125 189.234678 \r\nL 364.903125 188.871673 \r\nL 364.903125 188.508668 \r\nL 364.903125 188.145663 \r\nL 364.903125 187.782658 \r\nL 364.903125 187.419653 \r\nL 364.903125 187.056648 \r\nL 364.903125 186.693643 \r\nL 364.903125 186.330638 \r\nL 364.903125 185.967633 \r\nL 364.903125 185.604628 \r\nL 364.903125 185.241623 \r\nL 364.903125 184.878618 \r\nL 364.903125 184.515613 \r\nL 364.903125 184.152608 \r\nL 364.903125 183.789603 \r\nL 364.903125 183.426598 \r\nL 364.903125 183.063593 \r\nL 364.903125 182.700588 \r\nL 364.903125 182.337583 \r\nL 364.903125 181.974578 \r\nL 364.903125 181.611573 \r\nL 364.903125 181.248568 \r\nL 364.903125 180.885563 \r\nL 364.903125 180.522558 \r\nL 364.903125 180.159553 \r\nL 364.903125 179.796548 \r\nL 364.903125 179.433543 \r\nL 364.903125 179.070538 \r\nL 364.903125 178.707533 \r\nL 364.903125 178.344528 \r\nL 364.903125 177.981523 \r\nL 364.903125 177.618518 \r\nL 364.903125 177.255513 \r\nL 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287.844083 101.568968 \r\nL 287.604769 101.568968 \r\nL 287.365455 101.568968 \r\nL 287.126141 101.568968 \r\nL 286.886828 101.568968 \r\nL 286.647514 101.568968 \r\nL 286.4082 101.568968 \r\nL 286.168886 101.568968 \r\nL 285.929572 101.568968 \r\nL 285.690259 101.568968 \r\nL 285.450945 101.568968 \r\nL 285.211631 101.568968 \r\nL 284.972317 101.568968 \r\nL 284.733003 101.568968 \r\nL 284.49369 101.568968 \r\nL 284.254376 101.568968 \r\nL 284.015062 101.568968 \r\nL 283.775748 101.568968 \r\nL 283.536435 101.568968 \r\nL 283.297121 101.568968 \r\nL 283.057807 101.568968 \r\nL 282.818493 101.568968 \r\nL 282.579179 101.568968 \r\nL 282.339866 101.568968 \r\nL 282.100552 101.568968 \r\nL 281.861238 101.568968 \r\nL 281.621924 101.568968 \r\nL 281.38261 101.568968 \r\nL 281.143297 101.568968 \r\nL 280.903983 101.568968 \r\nL 280.664669 101.568968 \r\nL 280.425355 101.568968 \r\nL 280.186041 101.568968 \r\nL 279.946728 101.568968 \r\nL 279.707414 101.568968 \r\nL 279.4681 101.568968 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_decision_boundary(dt_clf, axis=[0.5, 7.5, 0, 3])\n",
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.scatter(X[y==2,0], X[y==2,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模拟使用基尼系数划分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from math import log\n",
    "\n",
    "def split(X, y, d, value):\n",
    "    index_a = (X[:,d] <= value)\n",
    "    index_b = (X[:,d] > value)\n",
    "    return X[index_a], X[index_b], y[index_a], y[index_b]\n",
    "\n",
    "def gini(y):\n",
    "    counter = Counter(y)\n",
    "    res = 1.0\n",
    "    for num in counter.values():\n",
    "        p = num / len(y)\n",
    "        res -= p**2\n",
    "    return res\n",
    "\n",
    "def try_split(X, y):\n",
    "    \n",
    "    best_g = float('inf')\n",
    "    best_d, best_v = -1, -1\n",
    "    for d in range(X.shape[1]):\n",
    "        sorted_index = np.argsort(X[:,d])\n",
    "        for i in range(1, len(X)):\n",
    "            if X[sorted_index[i], d] != X[sorted_index[i-1], d]:\n",
    "                v = (X[sorted_index[i], d] + X[sorted_index[i-1], d])/2\n",
    "                X_l, X_r, y_l, y_r = split(X, y, d, v)\n",
    "                p_l, p_r = len(X_l) / len(X), len(X_r) / len(X)\n",
    "                g = p_l * gini(y_l) + p_r * gini(y_r)\n",
    "                if g < best_g:\n",
    "                    best_g, best_d, best_v = g, d, v\n",
    "                \n",
    "    return best_g, best_d, best_v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "best_g = 0.3333333333333333\nbest_d = 0\nbest_v = 2.45\n"
    }
   ],
   "source": [
    "best_g, best_d, best_v = try_split(X, y)\n",
    "print(\"best_g =\", best_g)\n",
    "print(\"best_d =\", best_d)\n",
    "print(\"best_v =\", best_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1_l, X1_r, y1_l, y1_r = split(X, y, best_d, best_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.0"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "gini(y1_l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.5"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "gini(y1_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "best_g = 0.1103059581320451\nbest_d = 1\nbest_v = 1.75\n"
    }
   ],
   "source": [
    "best_g2, best_d2, best_v2 = try_split(X1_r, y1_r)\n",
    "print(\"best_g =\", best_g2)\n",
    "print(\"best_d =\", best_d2)\n",
    "print(\"best_v =\", best_v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2_l, X2_r, y2_l, y2_r = split(X1_r, y1_r, best_d2, best_v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.1680384087791495"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "gini(y2_l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.04253308128544431"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "gini(y2_r)"
   ]
  }
 ],
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